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Unformatted text preview: Math136 Review for exam 1 Summer 2010 1. Suppose R is the region in the first quadrant bounded by the curves y = 1 x , y = x 2 27 and x = 1. Set up and evaluate an integral whose value is (a) the area or R . (b) the volume of the solid resulting when revolving R about the x- axis. (c) the volume of the solid resulting when revolving R about the y- axis. 2. Find the volume of the solid S obtained by revolving the region enclosed by x = 0, x = 1, y = 0, and y = e x , about the y- axis. 3. Compute the future value of an account earning interest at a rate of 7% 5 years from now if money is deposited at a rate of f ( t ) = 10 + 3 t dollars per year. 4. The base of a solid S is the region on the xy plane enclosed by the semicircle above the x- axis x 2 + y 2 = 4. Its cross sections perpendicular to the y- axis are rectangles with height half the base. Find the volume of the solid S . 5. (a) Use the trapezoidal rule with n = 6 to give an approximation to Z 1 e- x 2 dx (b) How large has to be n...
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